Symbolic and interval rational interpolation: the problem of unattainable dataSymbolic and interval rational interpolation: the problem of unattainable data

Author

Salazar Celis, O.

Cuyt, A.

Van Deun, J.

Faculty/Department

Faculty of Sciences. Mathematics and Computer Science

Publication type

article

Publication

2008New York
, 2008

Subject

Mathematics

Source (journal)

AIP conference proceedings / American Institute of Physics. - New York

Volume/pages

1048(2008)
, p. 466-469

ISSN

0094-243X

ISI

000259567000111

Carrier

E

Target language

English (eng)

Affiliation

University of Antwerp

Abstract

A typical problem with rational interpolation is that of a so-called unattainable point, when the interpolation condition cannot be met by the rational interpolant of the specified degree. The problem can be dealt with in at least two approaches, one of which is novel and practically oriented. We admit infinity in the independent variable as well as in the function value. Rational interpolation is solved symbolically in its full generality by Van Barel and Bultheel [9]. The authors return a parameterized set of rational interpolants of higher degree than requested but without unattainable points. In many practical applications however, observations are not exact but prone to imprecise measurements. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. It is shown in [1] how a rational function of lowest complexity can be obtained which intersects all uncertainty intervals and avoids the typical problem of unattainable data.